Issue34

G Meneghetti et alii, Frattura ed Integrità Strutturale, 34 (2015) 109-115; DOI: 10.3221/IGF-ESIS.34.11 113 Several refined FE analyses have been carried out on the same cracked plates taken into consideration in the previous paragraph, with the aim to evaluate the local SED averaged over a control volume centred at the crack tip. Different geometrical combinations have been considered, varying the length 2a and the inclination ϕ of the crack (i.e. the mode mixity), while the radius of the control volume R 0 has been kept constant and equal to 0.1 mm. 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 10 100 a/d K* FE , K** FE K*FE K**FE +3% -3% 1.38  6 2  = 0°  = 10° 3.38 +3% -3%  12 (a) * FE * FE 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 10 100 a/d K* FE , K** FE K*FE K**FE +3% -3% 1.38  4 2  = 0°  = 30° 3.38 +3% -3%  14 * FE K** FE (b) 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 10 100 a/d K* FE , K** FE K*FE K**FE +3% -3% 1.38  5 2  = 0°  = 45° 3.38 +3% -3%  21 (c) K* FE K** FE 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 10 100 a/d K* FE , K** FE K*FE K**FE +3% -3% 1.38  3 2  = 0°  = 60° 3.38 +3% -3%  16 K* FE K** FE (d) Figure 3 : Calibration of the PSM approach for a crack (2α = 0°) under mixed mode (I+II) loading: (a) ϕ = 10°; (b) ϕ = 30°; (c) ϕ = 45°; (d) ϕ = 60°. Non-dimensional SIFs related to mode I and mode II. The mode mixity ratio (MM) has been evaluated according to the following definition: II I II K MM K K   (7) Eq. (7) provides as master cases MM = 0 for pure mode I with ϕ = 0°, MM = 0.5 for mixed mode with ϕ = 45° and MM = 1 for pure mode II loading. In all cases the numerical values of the SED calculated from the FE analyses have been compared with those analytically obtained by using the expressions for the SED based on the elastic peak stresses, Eq. (6), in order to verify the range of applicability of the proposed method. Being the exact values of the SIFs available, the mean value of the SED has been evaluated also according to Eq. (3). In particular the maximum difference between the SED parameter evaluated analytically (Eq. (3)) and numerically (by FEM) resulted about 5%, that means that the influence of higher order terms, as the T-stress, can be neglected in these cases, at least from an engineering point of view. The ratio between the SED based on the elastic peak stresses (Eq. 6, PSM W ) and the SED calculated from the FE analyses ( FEM W ) has been reported in Fig. 4, with reference to an inclination ϕ of the crack equal to 0°, 30°, 45° and 60°. From Fig. 4, it can be observed that the ratio / PSM FEM W W converges to unity, within a scatter band of ±10% for all different mode mixities taken into consideration. This occurs for a ratio a/d greater than 3 for the case MM = 0 ( ϕ = 0°), 8.50 for